Density plot of all sampled particles in the action space (J_ϕ, J_z). Left: Original sample of stars currently in the selection box (black rectangle): 1005 km s⁻¹kpc ≤ J_ϕ ≤ 2010 km s⁻¹kpc and 0.175 km s⁻¹kpc ≤ J_z ≤ 437.5 km s⁻¹kpc. Middle: Sampled particles 6 Gyr ago in model (ii) of a constant bar with spiral arms. They remain similar to their initial distribution in the left panel. Right: Particles in model (iv) of a decelerating bar with spiral arms. They have a more extended distribution J_ϕ 6 Gyr ago in this model. Some low-J_ϕ particles (J_ϕ ≲ 1000 km s⁻¹kpc) have gained rotation from the bar, but represent only a small fraction of the entire sample.